雜湊函數在密碼學上扮演奏重要的原始角色。它可被用來解決很多問題，包括驗證、確保資料完整以及改善數位簽章的效率。雜湊函數能將任意長度的文件壓縮成一個很小的固定長度，稱之為此文件的文件摘要。一個好的雜湊函數必須易於使用、瞭解以及能夠對抗密碼學上的侵略、破壞。此外，它的執行速度必須夠快。本篇論文首先分析四種有名的雜湊函數：Snefru、MD4、MD5、SHA。然後我們嘗式融合Snefru、MD4、MD5雜湊函數的優點，將SHA加以改進。結果產生一個新的雜湊函數，SHA+。這裡，SHA+所用的布林函數是選自HAVAL雜湊函數中所提到的布林函數，因為它們滿足一些密碼學上的重要特性。模擬結果顯示，SHA+比SHA更安全，而有它的執行速度大約是SHA的兩倍。

　　A one-way hash function is an important cryptographic primitive. It can be used not only to solve a wide variety of problems involving authentication, and data integrity, but also to improve the efficiency of digital signature. One-way hash functions compress a message of arbitrary length into a small fixed size output. The output value represents the message digest of the message. A good one-way hash function should be easy to use, understand, and ,above all, resist to cryptographic attacks. Also, its running speed should be fast when implemented in software. In this thesis, we first analyze four hash functions: Snefru, MD4,MD5, and SHA. Then, we try to enhance SHA by incorporating all the merits found in the other three hash functions been studied. This results in a new hash function, SHA+ .Here, the boolean functions used in SHA+ are selected from HAVAL, since they can meet some important primitive cryptographic properties. Simulation results indicate that SHA+ is securer than SHA, and is about 89% faster than SHA.